Firstly, I have a SEM model with two endogenous variables (categorical indicators) three exogenous/endogeous variables (continuous indicators), two exogenous variables (continuous indicators) and two observed continuous exogenous variables. N=1,500 and two groups.

1) the default estimator is WLSMV - if my variables (besides the ones indicated by categorical variables) are reasonably normally distributed what other estimators would be suitable? (any refs? I also have a weighting variable and missing data)

2) can i still use the missing data option? - and if yes, what method (FIML?) does it use?

3) How do i calculate power?

4) I have two groups and i want to see if a)the factor means (and means of observed exogenous variables) are different across groups and b) if the path co-efficients are different. Is this possibile? if yes, how do i do this? I get confused with which parameters to hold constant etc (refs welcomed here as well!

See the Topic 1 course handout on the website. The input for this comparison is shown at the end of the multiple group discussion. See also the video from Johns Hopkins March 2008 workshop on this topic.

I have discovered that i need to take a multiple group approach to testing group means - but i have a couple of extra questions.

I have 4 endogenous latent variables and 2 exogenous variables (in an SEM model). Do i have to do tests for measurement invariance/population heterogeneity for each latent variable in separate runs or can i test them all simultaneously? I ask because if there is VERY SLIGHT non-invariance across all the latent variables would these not all add up to show a worsening of the entire model fit? Thus leading one to conclude non-invariance when it is just a cumulative effect of small differences which on their own would still be invariant?

When testing for group mean differences one fixes the means of the second group to zero - Chi square tests then tell us if the means are different between the two groups. How can we tell which group had higher mean scores and to what degree?

Also, 2 of my latents have categorical indicators which makes it awkward for chi square diff tests when using WLSMV. is it OK to use the WLS estimator instead when just testing for invariance - then going back to WLSMV for testing direct/indirect relationships?

Please see Chapter 13 of the user's guide at the end of the multiple group section. The models for testing measurement invariance are described there. See also Topic 1 of the course handouts that are on the website where inputs are given for testing measurement invariance using multiple groups.

Yes, you can change WITH to ON. You might want to find an example in the user's guide closer to what you want and start with the input for the Monte Carlo counterpart of that example. Find an example with covariates to see how this is done.

yes, VERY time consuming! Is there another option for calculating power that isn't too complicated?

I am unable at this stage to update from version 4.21 to version 5.1 (i am currently in contact with tech support regarding this) so i am struggling a bit testing for measurement invariance across groups.

the problem is to do with the meanstructure command - more specifically when i add a meanstructure (as per the video) it makes no difference to the chi square and degrees of freedom. This is true regardless of whether factor loadings are constrained or free.

I'm sorry i don't understand. I am testing for measurement invariance across groups using the following commands but the error message i talked about earlier comes up. This command is based on your video at John Hopkins.

square brackets indicate a mean... "@" is not an equality constraint, instead it symbolizes "fixed at a certain value", e. g. zero. in sum: the means of rlit and math are fixed at zero. you should read more about the basics in the mplus manual.

Is it possible to test for invariance and heterogeneity when factor indicators are a mixture of continuous and categorical variables? (4 factors have continuous indicators and 2 factors have cat. indicators. All factors are continuous though.)

If yes can you still use a difftest with WLSMV?

I had a try combining the commands from handout 1 and 2 but with little success.

I have a 3 factor MGCFA. I want to compare the factor means. My model showed measurement invariance for loadings, thresholds, residuals, and factor variances BUT failed to show measurement invariance for the factor means.

Q1. does failure of invariance of the 'Factor Means' imply that the factor means are significantly different?

Q2. Should the model for testing measurement invariance for factor models be nested within the model testing meas inv for factor variance?

Q2. I understand that when comparing factor means I should use an unconstrained model. Should any other parameters, eg factor variances, also be unconstrained or just the factor means?

Factor means, variances, and covariances are not measurement parameters. They are structural parameters. Once you have established measurement invariance, you want to examine the structural parameter differences. You can do this using a series of nested models. Please see the Topic 1 course handout where this type of analysis is shown in detail.

Hello again, i am trying to get latent variable means and SDs (across differnt groups) using the tech4 output. However i notice that my LV means are negative across all the groups. The indicators were dichotomous and coded either 1 or 2.

the same thing happens when i try to get the latent mean for the whole sample (ie taking out the grouping option)

i have run a series of nested models to test for measurement invariance across 3 groups. Measurement Invariance was found. I then tested for Structural invariance of factor variances (found to be invariant) and then I tested for invariance of factor covariances (not found to be invariant).

I ran a final model to compare the 3 groups by setting factor variances to 1 and means to zero in a reference group and freely estimating variances and means in the other 2 groups. THis produced different factor variances for each group.

My questions are:

How can I find structural invariance for the factor variances but also produce different factor variances for each group when I run the final model (as described above)?

If i have found structural invariance of the factor variances, does it makes sense to compare variances across the groups as i have done in my final model?

even though the factor variances have been shown to be invariant, when I do the three group comparison and let the variance be freely estimated, the variances are different. One group has the smallest variance for all factors. Another group has the largest variance for a single factor.

Is valid to comment on why one group has the smallest variances, e.g. they are a more homogeneous group than the other groups? Or a characteristic of the other group has caused them to have the largest variance

If you concluded from your difference testing that the variances are invariant, the differences you see are not statistically significant. The differences you see are due to sampling variability not differences in the population.

On your website you give a fantastic example of how to test for group factor means differences - using a CFA example. In this case you do a difftest where step two constrains the second group mean to zero.

In SEM where factor means are endogenous, do you do the same or do you impose equality constraints on factor means instead? I notice in my tech4 that factor means are given for both groups, while an exogenous factor has 0 for the first group (like the CFA example).

To me this suggests i should impose an equality constraint on endoegous factors while constraining factor means at 0 for the exogenous factor. Is this correct?

Just to add to above. if i run just a CFA with latent variables and constrain group 2 factor means to zero - this shows up in tech 4 and everything works out fine

if i turn it into SEM (making factoros enodeogous and exogenous and adding covariates), the latent factor means in the first group are esimated, and constrining the factor means to zero in the second group does not change the means in tech4.

I think you are confusing means and intercepts. Means are estimated for exogenous factors. Intercepts are estimated for endogenous factors. TECH4 provides models estimated means, variances, and covariances for the factors in the model. I would have to see your output to fully understand what you are describing. If my comments are not sufficient, please send the outputs and your license number to support@statmodel.com.

In the model if a variable is endogenous, an intercept is estimated not a mean. TECH4 does not give intercepts. It gives means. Look at the output. I'm sorry I cannot help you further on this without going through support.